Texturing a line

you could, but it probably won't look right. Why not just use textured quads? Easy to implement, and it's probably your best bet.

GL_LINES as well as GL_POINT will be tetxured with current texture + current texturecoord (if texturing is enabled etc)
though as Morpheus011 saiz youre prolly best off with a strechted quad

Regardless, doesn't a line use the bounded texture as a 1D texture when rendered?

Use a quad. Fussing over the performance of sending two more vertices to the graphic card per bullet would be ridiculous unless you literally have millions of bullets at once. ;)

It wont really matter what method you use if the rendering will only be a couple of pixels wide. I do, however agree that you should use a textured quad. It really isnt all that difficult to set up and they look pretty good.